The project deals with three loosely interconnected areas of
mathematics. We obtained a number of outstanding results in the
theory of Thom polynomials, and more generally, in equivariant
obstruction theory. In particular, the introduction of Thom series,
and the calculation of the Thom polynomials of Morin singularities are
the most important advances in the subject in the last few years. On
the more geometric side, we made serious progress in the
description of the geometry of hyperkahler moduli spaces, and proved
the Batyrev-Materov mirror residue conjecture for toric orbifolds.
Finally, the more algebraic results of our project include discovering
new characteristic-2 phenomena in the representation theory of the
orthogonal group, and proving the Zamolodchikov periodicity conjecture
for Y-systems. We also found new algebraic inequalities for
semidefinite matrices, and using these, improved the best known lower
bound on products of real linear functionals.